Gacha Pity Simulator

What this generator does

Derives the chance of the first hit landing on each pull from the rate curve, works out the mean and median from that, then simulates the same system and reports whether the two agree.

How to use this tool

1. Pick one of the systems, or set your own base chance, climb point and guarantee.
2. Choose how many runs to simulate. More runs make the check tighter, not the answer different.
3. Read the expected pulls per hit and the rate you would actually see.
4. Compare that rate with the advertised one; the multiple between them is what the pity counter is worth.
5. If the system splits hits with a featured item, read the second figure: that is what the one you want costs.

Understanding the controls

System

A few systems of familiar shapes, or your own: a base chance, the pull the odds start climbing at, the pull a hit is guaranteed, and whether half of all hits are the wrong item.

Runs to simulate

How many times to play the system out. A hundred thousand runs pins the simulated mean to within a twentieth of a pull; a thousand is enough to see the shape.

Seed (optional)

Type anything to repeat the same simulation. That is what a seed does here — it makes a run reproducible, and has nothing to do with cryptographic strength.

Common use cases

• Working out what a quoted rate means before deciding anything
• Comparing two systems whose advertised rates look similar
• Seeing how much of the real rate comes from soft pity rather than the base chance
• Checking a claim someone has made about expected pulls
• Understanding why a guarantee at the end changes the average so much

How this generator works

Two independent routes to the same number, which is what makes the answer trustworthy. The first is arithmetic: the chance of the first hit landing on pull one is the rate on pull one; on pull two, the chance of missing the first multiplied by the rate on the second; and so on. Because the last pull is a guarantee, those chances add up to exactly one, which is checked. The average and the halfway point follow directly. The second route is to play the system out many times and take the mean. Neither is derived from the other, so if either were wrong they would disagree — and they are compared before anything is shown, against a band of four standard errors, which a correct simulation strays outside about once in sixteen thousand. The cost of a featured item is worked out rather than measured too: losing the coin toss guarantees the next hit, so a copy costs one hit half the time and two the other half, which is one and a half hits whatever the rate curve looks like.

Randomness and fairness

The simulated pulls come from your browser's cryptographic random source. A seed replaces it with a repeatable one so you can quote a run and have someone else reproduce it — the seed is for reproducibility, not cryptographic strength.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• The climb from soft pity to the guarantee is assumed to be a straight line; no real game publishes its curve, and this does not claim to have measured one.
• Nothing here is about a particular game, and no figures are taken from one.
• The featured split is modelled as an even coin toss with a guarantee on the next hit, which is the common shape but not the only one.
• This is arithmetic about odds, not advice about spending money.

Privacy and your data

Every pull is simulated in your browser. Nothing you type as a seed, no system you describe and no result leaves the device.